中文摘要：

Walsh-Haar函数系是一种具有良好的全局／局部性质的函数系，与其对应的离散变换是一种正交变换，有着广阔的应用前景。该文给出了离散Walsh-Haar变换及其逆变换的定义，并运用二分技术得到了离散Walsh-Haar变换的快速算法。文中的设计思想和方法可用于研究其它序的离散Walsh-Haar变换和其它的正交变换的快速算法。

英文摘要：

Walsh-Haar function system is a new kind of function systems that has good global/local property. Discrete Walsh-Haar transformation is an orthogonal transformation that can be widely used in signal processing. In this paper, a new type of transformation,discrete Walsh-Haar transformation, is proposed, and the fast algorithm of discrete Walsh-Haar transformation is studied based on the dichotomous technique. The idea and method used to design the fast algorithm in this paper can be used to study the fast algorithms of other order discrete Walsh-Haar transformations and other discrete orthogonal transformations.